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Evaluate the determinants in(i) |(costhe...

Evaluate the determinants in(i) `|(costheta,-sintheta),(sintheta,costheta)|` (ii) `|(x^2-x+1,x-1),(x+1,x+1)|`

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To evaluate the given determinants, we will follow the standard formula for a 2x2 determinant. The determinant of a matrix \[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \] ...
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Evaluate the determinants in |{:(costheta,-sintheta),(sintheta,costheta):}|

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Knowledge Check

  • Determinant A=|(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)|

    A
    Independent of `theta`
    B
    dependent of `theta`
    C
    dependent of `theta` and x
    D
    None of the above

  • If A=[(costheta,-sintheta),(sintheta,costheta)] " then " A^(-1) =?

    A
    A
    B
    `-A`
    C
    adjA
    D
    `=-adjA`

  • (sintheta-costheta+1)/(sintheta+costheta-1) is equal to

    A
    `(1)/(tan theta - sec theta)`
    B
    `(1)/(sec theta - tan theta)`
    C
    `(1)/(cos theta - tan theta)`
    D
    `(1)/(tan theta - cos theta)`

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